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Then the vector =, called the scattering vector or transferred wave vector, measures the difference between the incoming and outgoing wave vectors. The three conditions that the scattering vector Δ k {\displaystyle \mathbf {\Delta k} } must satisfy, called the Laue equations , are the following:
In many areas of science, Bragg's law, Wulff–Bragg's condition, or Laue–Bragg interference are a special case of Laue diffraction, giving the angles for coherent scattering of waves from a large crystal lattice. It describes how the superposition of wave fronts scattered by lattice planes leads to a strict relation between the wavelength ...
The momentum transfer plays an important role in the evaluation of neutron, X-ray, and electron diffraction for the investigation of condensed matter. Laue-Bragg diffraction occurs on the atomic crystal lattice, conserves the wave energy and thus is called elastic scattering, where the wave numbers final and incident particles, and , respectively, are equal and just the direction changes by a ...
Scattering also includes the interaction of billiard balls on a table, the Rutherford scattering (or angle change) of alpha particles by gold nuclei, the Bragg scattering (or diffraction) of electrons and X-rays by a cluster of atoms, and the inelastic scattering of a fission fragment as it traverses a thin foil.
Consider the scattering of a beam of wavelength by an assembly of particles or atoms stationary at positions , =, …,.Assume that the scattering is weak, so that the amplitude of the incident beam is constant throughout the sample volume (Born approximation), and absorption, refraction and multiple scattering can be neglected (kinematic diffraction).
However, both scattering and diffraction are related general phenomena and the distinction has not always existed. Thus Guinier 's classic text [ 1 ] from 1963 is titled "X-ray diffraction in Crystals, Imperfect Crystals and Amorphous Bodies" so 'diffraction' was clearly not restricted to crystals at that time.
As with other diffraction methods, the sample is scanned in a wide-angle X-ray goniometer, and the scattering intensity is plotted as a function of the 2θ angle. X-ray diffraction is a non destructive method of characterization of solid materials.
The Mott scattering is the theoretical diffraction pattern produced by such a mathematical model. It is used as the beginning point in calculations in electron scattering diffraction studies. The equation for the Mott cross section includes an inelastic scattering term to take into account the recoil of the target proton or nucleus.
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